2000 VW Overheating

I recently purchased a 2000 VW Beetle with a 1.8 Turbo engine, on the way home the red light came on telling us that the car was overheating, we got it home and took it apart to find that the thermostat and water pump were in horrible condition. We replaced them both and the timing belt and took it for a drive and the blue light stayed on the entire time. This morning we decided to drive it to church and the red light came on again, we made it to church and by the time we came back out to leave it had leaked all of the water.
Has anyone else had this sort of problem? We're going crazy trying to fix it so any help that you could give me would really mean a lot.
Thank you in advance!

If all the water leaked out when you were in church then just where did it leak from? Maybe you did not completely fill the radiator and overflow tank after you changed the pump. The blue light means the engine is cold.